Steric-effect induced alterations in streaming potential and energy transfer efficiency of non-newtonian fluids in narrow confinements

Streaming Potential and Associated Electrokinetic Effects through a Channel Filled with Electrolyte Solution Surrounded by a Layer of Immiscible and Dielectric Liquid

The present article deals with the streaming potential-mediated pressure-driven flow across a channel in which the electrolyte solution is surrounded by a layer of cell membrane. Such a membrane of a biological cell may be modeled as an immiscible and dielectric liquid, which may bear free lipid molecules or charged surfactants. The presence of such additional charged molecules may lead to formation of liquid-liquid interfacial charge. In addition, the dielectric gradient-mediated ion partitioning effect further plays an important role in two-phase electrokinetic motion. We aim to study the generation of streaming potential and electrokinetic conversion efficiency as well as associated electroviscous effect for the undertaken problem. The mathematical model is based on the Poisson-Boltzmann equation for electrostatic potential and the Stokes equation for fluid flow, and the problem is studied considering suitable interfacial conditions for the flow variables along the liquid-liquid interface. The explicit analytical results for velocity and streaming field, electrokinetic energy conversion efficiency, and the parameter indicating the electroviscous effect are derived under the Donnan limit and within the Debye-Hückel electrostatic framework. We further numerically calculated the aforementioned intrinsic electrokinetic parameter associated with the problem undertaken for a wide range of pertinent parameters. The results are illustrated to indicate the impact of pertinent parameters on the generation of the streaming potential and associated electrokinetic effects.

Rheology-modulated alterations in electro-magneto-hydrodynamic flows in a narrow cylindrical capillary: Contrasting trends in high and low surface charge limits

We investigate electrokinetic transport of power-law fluids in a narrow cylindrical capillary in the presence of a transverse magnetic field. The governing equations including the full Poisson-Boltzmann equation and the Cauchy momentum equation with power-law constitutive behavior are solved numerically, without being restrictive to low surface potential limits. The influence of the power-law index, wall zeta potential, relative strength of electromagnetic force over viscous force (as represented by the Hartmann number), and the lateral electric field strength on the variation of the volumetric flow rate is analyzed. Our results reveal a significant augmentation in the net-throughput beyond the traditionally explored low surface-charge limits, especially for shear-thinning fluids, defying the established notions. These fundamental theoretical premises may act as essential precursors towards developing deeper insights on fluidic transport bio-nanopores under electro-magneto- hydrodynamic influences.

Electrokinetics of polymeric fluids in narrow rectangular confinements

The flow of polymeric liquids in narrow confinements with a rectangular cross section, in the presence of electrical double layers is analyzed here. Our analysis is motivated by the fact that many of the previous studies on the flow of complex fluids tend to focus on highly idealized parallel plate channels, which are markedly different from the rectangular ducts, used in many experiments and devices. We consider the combined electroosmotic and pressure driven flows as well as the streaming potential resulting from a mechanically driven flow. We use two distinct constitutive relations to model the polymeric liquids, namely the simplified exponential Phan-Thien-Tanner (sePTT) model and the Giesekus model, both of which are non-linear viscoelastic models, capable of capturing the shear thinning behavior. We establish that the applied electric field may have a strong influence on the overall flow rate, which rapidly increases with the field strength as well as the extent of viscoelasticity of the fluid. Viscoelasticity and shear thinning behavior also enhance the streaming potential by several fold as compared to a Newtonian medium. We demonstrate that the aspect ratio of a channel has a bigger influence on the net throughput and the streaming potential, when the extent of viscoelasticity is relatively large. We illustrate that for sePTT fluids, the flow is strictly unidirectional, while for Giesekus fluids, secondary flows are inevitably present on account of their non-zero second normal stress coefficient. Although the electric field does not change the overall patterns of these secondary flows, their magnitude does depend on the imposed field strength for combined flows.

Numerical study of the vortex-induced electroosmotic mixing of non-Newtonian biofluids in a nonuniformly charged wavy microchannel: Effect of finite ion size

We propose a micromixer for obtaining better efficiency of vortex induced electroosmotic mixing of non-Newtonian bio-fluids at a relatively higher flow rate, which finds relevance in many biomedical and biological applications. To represent the rheology of non-Newtonian fluid, we consider the Carreau model in this study, while the applied electric field drives the constituent components in the micromixer. We show that the spatial variation of the applied field, triggered by the topological change of the bounding surfaces, upon interacting with the non-uniform surface potential gives rise to efficient mixing as realized by the formation of vortices in the proposed micromixer. Also, we show that the phase-lag between surface potential leads to the formation of asymmetric vortices. This behavior offers better mixing performance following the appearance of undulation on the flow pattern. Finally, we establish that the assumption of a point charge in the paradigm of electroosmotic mixing, which is not realistic as well, under-predicts the mixing efficiency at higher amplitude of the non-uniform zeta potential. The inferences of the present analysis may guide as a design tool for micromixer where rheological properties of the fluid and flow actuation parameters can be simultaneously tuned to obtain phenomenal enhancement in mixing efficiency.

Streaming potential in bio-mimetic microvessels mediated by capillary glycocalyx

Implantable medical devices and biosensors are pivotal in revolutionizing the field of medical technology by opening new dimensions in the field of disease detection and cure. These devices need to harness a biocompatible and physiologically sustainable safe power source instead of relying on external stimuli, overcoming the constraints on their applicability in-vivo. Here, by appealing to the interplay of electromechanics and hydrodynamics in physiologically relevant microvessels, we bring out the role of charged endothelial glycocalyx layer (EGL) towards establishing a streaming potential across physiological fluidic conduits. We account for the complex rheology of blood-mimicking fluid by appealing to Newtonian fluid model representing the blood plasma and a viscoelastic fluid model representing the whole blood. We model the EGL as a poroelastic layer with volumetric charge distribution. Our results reveal that for physiologically relevant micro-flows, the streaming potential induced is typically of the order of 0.1 V/mm, which may turn out to be substantial towards energizing biosensors and implantable medical devices whose power requirements are typically in the range of micro to milliwatts. We also bring out the specific implications of the relevant physiological parameters towards establishment of the streaming potential, with a vision of augmenting the same within plausible functional limits. We further unveil that the dependence of streaming potential on EGL thickness might be one of the key aspects in unlocking the mystery behind the angiogenesis pattern. Our results may open up novel bio-sensing and actuating possibilities in medical diagnostics as well as may provide a possible alternative regarding the development of physiologically safe and biocompatible power sources within the human body.

Streaming-potential-mediated pressure-driven transport of Phan-Thien-Tanner fluids in a microchannel

Streaming potential mediated pressure driven electrokinetic transport of Phan-Thien-Tanner fluids in a slit type parallel plate microchannel is studied analytically and semianalytically. Without adopting the traditional considerations of Debye-Hückel linearization approximation for low surface potentials, exact analytical solutions are obtained for the electrostatic potential distribution, velocity, and volumetric flow rates taking into account the full Poisson-Boltzmann equation. The influences of interfacial electrokinetics and viscoelasticity on the streaming potential development, polymeric stress components, shear viscosity, and the hydroelectric energy conversion efficiency are incorporated concurrently. Major findings indicate that the magnitude of the induced streaming potential, volumetric flow rates, and the energy conversion efficiency increases up to a threshold limit of zeta potential of ζ≤6, however, it follows an asymptotic reduction at the other end of higher zeta potentials 6<ζ≤10. The polymeric stress components and shear viscosity follow a similar trend in the regime of 1≤ζ≤10, which is primarily governed by the streaming potential field. In contrast, the transverse averaged shear viscosity in the range 1≤ζ≤10 obeys an opposite trend by yielding an inverted parabolic shape. Amplification in the Stern layer conductivity yields a progressive reduction in the streaming potential magnitude and the hydroelectric energy conversion efficiency. The effect of the fluid viscoelasticity designated by the Weissenberg number exhibits a linear enhancement in streaming potential, flow rates, and the energy conversion efficiency. Moreover, we show that with the optimal combinations of surface charging and fluid viscoelasticity, it is possible to accomplish a giant augmentation in the hydroelectric energy conversion efficiency and flow rates. The analytical and semianalytical results presented in this investigation are believed to be worthy not only to cater deeper understanding in micro- and nanofluidic transport characteristics but also will act as functional design instrument for the future generation of energy efficient narrow fluidic devices.

The effect of the finite size of ions and Debye layer overspill on the screened Coulomb interactions between charged flat plates

Screened repulsion between uniformly charged plates with an intervening electrolyte is analyzed for strongly overlapped electrical double layers (EDL), accounting for the steric effect of ions and their expulsion from EDL edges into the surrounding solution. As a generalization of a study by Philipse et al. which does not account for these effects, an analytical expression is derived for the repulsion pressure in the limit of infinitely long plates with a zero-field assumption, which agrees closely with the corresponding numerical solution at low inter-plate separations. Our results show an augmented repulsive pressure for finite-sized ions at strong EDL overlaps. For plates with a finite lateral size, we demonstrate a further extended domain of low inter-plate gaps where the repulsion pressure increases with ion size due to a strong interplay between the steric interaction of ions and the EDL overspill phenomenon, considered earlier in a study by Ghosal & Sherwood limited to the linear Debye-Hückel regime (which cannot account for the steric effect of ions). This investigation on a simple model should enhance our understanding of the interaction between charged particles in electrophoresis, nanoscale self-assembly, active particles, and various other electrokinetic systems.

Patterned surface charges coupled with thermal gradients may create giant augmentations of solute dispersion in electro-osmosis of viscoelastic fluids

Augmenting the dispersion of a solute species and fluidic mixing remains a challenging proposition in electrically actuated microfluidic devices, primarily due to an inherent plug-like nature of the velocity profile under uniform surface charge conditions. While a judicious patterning of surface charges may obviate some of the concerning challenges, the consequent improvement in solute dispersion may turn out to be marginal. Here, we show that by exploiting a unique coupling of patterned surface charges with intrinsically induced thermal gradients, it may be possible to realize giant augmentations in solute dispersion in electro-osmotic flows. This is effectively mediated by the phenomena of Joule heating and surface heat dissipation, so as to induce local variations in electrical properties. Combined with the rheological premises of a viscoelastic fluid that are typically reminiscent of common biofluids handled in lab-on-a-chip-based micro-devices, our results demonstrate that the consequent electro-hydrodynamic forcing may open up favourable windows for augmented hydrodynamic dispersion, which has not yet been unveiled.

Efficient electrochemomechanical energy conversion in nanochannels grafted with end-charged polyelectrolyte brushes at medium and high salt concentration

We develop a theory to study the generation of the streaming potential and the resulting electrochemomechanical energy conversion (ECMEC) in the presence of pressure-driven transport in nanochannels grafted with end-charged polyelectrolyte (PE) brushes. Our theory gives a thermodynamically self-consistent coupled description of the PE-brush and the electrostatics of the electric double layer (EDL) induced by the PE charges. The end-charged brushes localize the maximum EDL charge density away from the wall, thereby enabling a larger magnitude of pressure-driven transport to stream the ions downstream. This effect is retarded by the drag force imparted by the brushes as well as by the enhanced electroosmotic transport in a direction opposite to the pressure-driven transport. An interplay of these three issues leads to highly non-trivial electrohydrodynamic transport that eventually allows us to converge on appropriate properties of the brushes (e.g., grafting density and the number of monomers) that lead to the generation of a significantly larger streaming potential and a much improved efficiency of the ECMEC as compared to the brush-free nanochannels particularly at medium and high salt concentrations.

Softness Induced Enhancement in Net Throughput of Non-Linear Bio-Fluids in Nanofluidic Channel under EDL Phenomenon

In this article, we describe the electro-hydrodynamics of non-Newtonian fluid in narrow fluidic channel with solvent permeable and ion-penetrable polyelectrolyte layer (PEL) grafted on channel surface with an interaction of non-overlapping electric double layer (EDL) phenomenon. In this analysis, we integrate power-law model in the momentum equation for describing the non-Newtonian rheology. The complex interplay between the non-Newtonian rheology and interfacial electrochemistry in presence of PEL on the walls leads to non-intuitive variations in the underlying flow dynamics in the channels. As such, we bring out the variations in flow dynamics and their implications on the net throughput in the channel in terms of different parameters like power-law index (n), drag parameter (α), PEL thickness (d) and Debye length ratio (κ/κ_PEL) are discussed. We show, in this analysis, a relative enhancement in the net throughput through a soft nanofluidic channel for both the shear-thinning and shear-thickening fluids, attributed to the stronger electrical body forces stemming from ionic interactions between polyelectrolyte layer and electrolyte layer. Also, we illustrate that higher apparent viscosity inherent with the class of shear-thickening fluid weakens the softness induced enhancement in the volumetric flow rate for the shear-thickening fluids, since the viscous drag offered to the f low f ield becomes higher for the transport of shear-thickening fluid.

Electroosmosis of Viscoelastic Fluids: Role of Wall Depletion Layer

We investigate electroosmotic flow of two immiscible viscoelastic fluids in a parallel plate microchannel. Contrary to traditional analysis, the effect of the depletion layer is incorporated near the walls, thereby capturing the complex coupling between rheology and electrokinetics. Toward ensuring realistic prediction, we show the dependence of electroosmotic flow rate on the solution pH and polymer concentration of the complex fluid. In order to assess our theoretical predictions, we have further performed experiments on electroosmosis of an aqueous solution of polyacrylamide (PAAm). Our analysis reveals that neglecting the existence of a depletion layer would result in grossly incorrect predictions of the electroosmotic transport of such fluids. These findings are likely to be of importance in understanding electroosmotically driven transport of complex fluids, including biological fluids, in confined microfluidic environments.

Electro-osmosis of nematic liquid crystals under weak anchoring and second-order surface effects

Advent of nematic liquid crystal flows has attracted renewed attention in view of microfluidic transport phenomena. Among various transport processes, electro-osmosis stands as one of the efficient flow actuation mechanisms through narrow confinements. In the present study, we explore the electrically actuated flow of an ordered nematic fluid with ionic inclusions, taking into account the influences from surface-induced elasticity and electrical double layer (EDL) phenomena. Toward this, we devise the coupled flow governing equations from fundamental free-energy analysis, considering the contributions from first- and second-order elastic, dielectric, flexoelectric, charged surface polarization, ionic and entropic energies. The present study focuses on the influence of surface charge and elasticity effects in the resulting linear electro-osmosis through a slit-type microchannel whose surfaces are chemically treated to display a homeotropic-type weak anchoring state. An optical periodic stripe configuration of the nematic director has been observed, especially for higher electric fields, wherein the Ericksen number for the dynamic study is restricted to the order of unity. Contrary to the isotropic electrolytes, the EDL potential in this case was found to be dependent on the external field strength. Through a systematic investigation, we brought out the fact that the wavelength of the oscillating patterns is dictated mainly by the external field, while the amplitude depends on most of the physical variables ranging from the anchoring strength and the flexoelectric coefficients to the surface charge density and electrical double layer thickness.

Consistent prediction of streaming potential in non-Newtonian fluids: the effect of solvent rheology and confinement on ionic conductivity

A consistent framework is developed to account for the solvent rheology and steric factor to obtain concentration-dependent ionic conductivity and streaming potential.

Drastic alteration of diffusioosmosis due to steric effects

We demonstrate essential quantitative and qualitative distinctions between the steric effects on classical electrokinetic phenomena like electroosmosis and on diffusioosmosis.

Ionic size dependent electroviscous effects in ion-selective nanopores

Pressure-driven flows of aqueous ionic liquids are characterized by electroviscosity-an increase in the effective (apparent) viscosity because of an induced back electric field termed streaming potential. In this work, we investigate the electrokinetic phenomenon of streaming potential mediated flows in ion-selective nanopores. We report a dramatic augmentation in the effective viscosity as attributable to the finite size effect of the ionic species in counterion-only systems. The underlying physics involves complex interaction between the concerned electrochemical phenomena and hydrodynamic transport in a confined fluidic environment, which we capture through a modified continuum based approach and validate using molecular dynamics simulations. We obtain an expression for the ionic-size dependent streaming potential pertinent to the physical situation being addressed. The corresponding estimations of effective viscosity implicate that the classical paradigm of point sized ions can give rise to gross underestimations of the flow resistance in counterion-only systems especially for negligible surface (Stern layer) conductivity and large fluidic slip at the surface.

Electrohydrodynamics within the electrical double layer in the presence of finite temperature gradients

A wide spectrum of electrokinetic studies is modeled as isothermal ones to expedite analysis even when such conditions may be extremely difficult to realize in practice. Going beyond the isothermal paradigm, we address here the case of flow induced electrohydrodynamics, commonly streaming potential flows, in a situation where finite temperature gradients do exist. By way of analyzing a model problem of flow through a narrow parallel-plate channel, we show that the temperature gradients applied at the channel walls may have a significant effect on the streaming potential, and, consequently, on the flow itself. Our model takes into consideration all the pertinent phenomenological aspects stemming from the imposed thermal gradients, such as the Soret effect, the thermoelectric effect, and the electrothermal effect, by a full-fledged coupling among the electric potential, the ionic species distribution, the fluid velocity and the local fluid temperature fields, without resorting to ad hoc simplifications. We expect this expository study to contribute significantly towards more sophisticated future endeavors in actual development of micro- and nano-devices for applications simultaneously involving thermal management and electrokinetic effects.

Exploring new scaling regimes for streaming potential and electroviscous effects in a nanocapillary with overlapping electric double layers

In this paper, we unravel new scaling regimes for streaming potential and electroviscous effects in a nanocapillary with thick overlapping Electric Double Layers (EDLs). We observe that the streaming potential, for a given value of the capillary zeta (ζ) potential, varies with the EDL thickness and a dimensionless parameter R, quantifying the conduction current. Depending on the value of R, variation of the streaming potential with the EDL thickness demonstrates distinct scaling regimes: one can witness a Quadratic Regime where the streaming potential varies as the square of the EDL thickness, a Weak Regime where the streaming potential shows a weaker variation with the EDL thickness, and a Saturation Regime where the streaming potential ceases to vary with the EDL thickness. Effective viscosity, characterizing the electroviscous effect, obeys the variation of the streaming potential for smaller EDL thickness values; however, for larger EDL thickness the electroosmotic flow profile dictates the electroviscous effect, with insignificant contribution of the streaming potential.

Influence of hydrophobic effects on streaming potential

We study the influence of hydrophobic effects on streaming potential mediated flow through a narrow confinement. In a clear departure from the approach used in prior works, we use a phase-field model to capture the hydrophobicity-induced depletion in the near wall region, and express the variation of viscosity and permittivity across the interfacial layer in terms of the phase-field variable. We then use these in the determination of the flow velocity, and highlight the sensitive interplay between the intrinsic length scale of the electrical double layer and that of the depletion in terms of the variations of an effective normalized viscosity that captures the electroviscous effect. We expect that this work will be an important step forward in the realistic continuum modeling of interfacial physics in the particular context of streaming potential mediated flows.

Electrokinetics over charge-modulated surfaces in the presence of patterned wettability: role of the anisotropic streaming potential

In the present study, we focus on evaluating the induced streaming electric field along the orthogonal directions in a narrow fluidic confinement in the presence of patterned surface wettability and modulated surface charges. We attempt to assess the implications of such modulations on the related important quantities and pinpoint the regimes of improved induced streaming potential field and the resulting anisotropy in the induced potential. Our results reveal that for certain combinations of the parameters characterizing the modulated slip, a significant amount of augmentation in the streaming electric field might be obtained, whereas in other cases the effects may lead to adverse consequences. We further demonstrate that the presence of anisotropic modulations on the channel walls give rise to considerable off-diagonal effects, which makes the streaming potential "disoriented" with the applied pressure gradient, when the same is not applied along one of the orthogonal directions. Our analysis also shows that one can remove such "mis-orientations" by finely tuning several relevant flow and geometric parameters, which may bear immense scientific and technological consequences towards an improved design of miniaturized energy conversion devices.

Effects of solvent-mediated nonelectrostatic ion-ion interactions on a streaming potential in microchannels and nanochannels

Here, we capture the consequences of solvent-mediated nonelectrostatic ion-ion interactions, coupled with the considerations of finite-sized effects of the ionic species, on electrokinetic transport in narrow fluidic confinements. We consider pressure-driven flow in microchannels and nanochannels in the presence of electrical double layer effects and analyze the establishment of a streaming potential as mediated by a Yukawa-like pair potential that integrates the ion specificity with the governing nonelectrostatic interactions. We bring out the influences of these interactions on electroviscous effects manifested due to the establishment of the streaming potential. Our considerations provide a plausible explanation for the gross overestimation of electrokinetic energy conversion efficiencies as predicted by classical electrical double layer theories that ignore nonelectrostatic interactions between the ionic species.

Highly enhanced energy conversion from the streaming current by polymer addition

In this contribution, we present for the first time the experimental results of energy conversion from the streaming current when a polymer is added to the working solution. We added polyacrylic acid (PAA) in concentrations of 200 ppm to 4000 ppm to a KCl solution. By introducing PAA, the input power, which is the product of volumetric flow rate and the applied pressure, reduced rapidly as compared to the case of using only a normal viscous electrolyte KCl solution. The output power at the same time remained largely constant, whereby an increase of the streaming current and a decrease of the streaming potential simultaneously occurred. These combined factors led to the massive increase of the energy conversion efficiency. Particularly, the results showed that when PAA was in a 0.01 mM KCl solution, the energy conversion efficiency of the system was enhanced by a factor of 447 (±2%), as compared to the case of the solution containing only 0.01 mM KCl. An enhancement factor of 249 (±4%) was also observed when PAA was added to the higher ionic strength background solution, 1 mM KCl. This finding can have practical use in microchannel-array energy conversion systems. When, instead of the negatively charged PAA, a non-ionic polymer polyethylene oxide (PEO) was added to the solution, no efficiency increase was observed, probably due to polymer wall adsorption.

Combined effects of interfacial permittivity variations and finite ionic sizes on streaming potentials in nanochannels

In this work, we investigate the effects of local permittivity variations, induced by a preferential orientation and exclusion of water dipoles close to channel walls, and the effects of finite-sized ions on the induced streaming potential in nanochannels. We make a detailed analysis of the underlying physicochemical interactions by considering combinations of cases where ions are considered to be point sized/finite sized and permittivity variation effects to be present/absent. By accounting for the dielectric friction (which in turn is a function of the local permittivity) in addition to the classical Stokes friction, we show that for high interfacial potentials and narrow confinements, the induced streaming potential field for the cases in which the polarization effects are considered for finite-sized ions is remarkably higher than for the cases in which the polarization effects are neglected. Thus, by coupling the nonlinear effects of finite-sized ions and water dipole polarization along with the dielectric friction, we open a new paradigm of streaming potential predictions for narrow fluidic confinements, bearing far-ranging scientific and technological consequences in nanoscale science and technology.

Consistent accounting of steric effects for prediction of streaming potential in narrow confinements

The traditional modeling framework for determining streaming potential, when taking into consideration finite size effects, suffers from an oversight in that while the model incorporates the size effects in the ion distribution profiles, it neglects these very same effects in the flux contributions, even though diffusivities are intrinsically linked with ionic friction, which again depends on the size of the ions. This oversight may lead to inconsistent quantitative estimates through ad hoc consideration of diffusivity values, apparently independent of the specific size of the ions, which nevertheless determines the ionic profiles. We remedy this theoretical inconsistency by expressing the diffusivity in terms of the ionic radius and investigate the consequences of such a description of the diffusivity-dependent flux, consistent with the ionic distribution profiles, on streaming potential mediated flow predictions. Additionally, we consider the effects of "charge induced thickening" so that both viscosity and diffusivity are expressed as spatially varying functions. As an unintuitive implication, we also show that calculation of nonzero values of streaming potential under the purview of classical Boltzmann distributions, which consider ions to be pointlike charges, is itself a theoretical inconsistency. We believe that the simple framework presented in this paper will pave the way for more sophisticated modeling efforts in the future.

Electrokinetically induced alterations in dynamic response of viscoelastic fluids in narrow confinements

We investigate a dynamical interplay between interfacial electrokinetics and a combined dissipative and elastic behavior of flow through narrow confinements, in analogy with spatiotemporal hydrodynamics of porous media. In particular, we investigate the effects of streaming potential on the pertinent dynamic responses, by choosing a Maxwell fluid model for representing the consequent electro-hydrodynamic characteristics. We transform the pertinent governing equation to the frequency domain, so that a dynamic generalization of Darcy's law in the presence of streaming potential effects can be effectively realized. We show that the frequencies corresponding to local maxima in the dynamic permeability also correspond to local maxima in the induced streaming potential. We also bring out the effects of Stern layer conductivity on the dynamic permeability. Our analytical estimates do reveal that serious overestimations in the commonly portrayed notion of massive amplifications of dynamic permeability at resonating frequencies may be possible, if interactions between spontaneous electrochemical interfacial phenomena and pulsating pressure-gradient-driven viscoelastic transport are trivially ignored.